At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

A rollercoaster cart that has a mass of 4500 kg has 67.5 kJ (kilojoules), or 67,500 J (joules), of gravitational potential
energy. What is its height above the ground?
PT.2
The same 4500 kg rollercoaster cart is moving with 63.0 kJ (kilojoules), or 63,000 J (joules), of kinetic energy at the
bottom of its biggest hill. What is its velocity?


Sagot :

Answer: The height of rollercoaster cart above the ground is 1.53 m.

The velocity of rollercoaster cart is 5.29 m/s.

Explanation:

Potential energy is the energy occupied by a substance due to its position. Formula for potential energy is as follows.

P.E = mgh

where,

m = mass of substance

g = gravitational constant = [tex]9.8 m/s^{2}[/tex]

h = height

Substitute the values into above formula as follows.

[tex]P.E = m \times g \times h\\67500 J = 4500 kg \times 9.8 m/s^{2} \times h\\h = \frac{67500 J}{4500 kg \times 9.8 m/s^{2}}\\= 1.53 m[/tex]

Hence, the height of rollercoaster cart above the ground is 1.53 m.

Kinetic energy is the energy occupied by the motion of a substance. Formula for kinetic energy is as follows.

[tex]K.E = \frac{1}{2}m \times v^{2}[/tex]

where,

m = mass of substance

v = velocity of substance

Substitute the values into above formula as follows.

[tex]K.E = \frac{1}{2}m \times v^{2}\\63000 J = \frac{1}{2} \times 4500 kg \times v^{2}\\v^{2} = \frac{63000 J \times 2}{4500 kg}\\v = 5.29 m/s[/tex]

Hence, the velocity of rollercoaster cart is 5.29 m/s.

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.